Surveys in Differential Geometry
Volume 18 (2013)
Mean curvature flows and isotopy problems
Pages: 227 – 235
In this note, we discuss the mean curvature flow of graphs of maps between Riemannian manifolds. Special emphasis will be placed on estimates of the flow as a non-linear parabolic system of differential equations. Several global existence theorems and applications to isotopy problems in geometry and topology will be presented. The results are based on joint works of the author with his collaborators I. Medoš, K. Smoczyk, and M.–P. Tsui.